A male 'neighborhood' cat discovered our doggie door one night in a horrible thunderstorm. Found him hiding under the bed, with our female making sure he stayed there.
After that I started seeing him hanging around more and more in the front yard (doggie door in the back door, fenced yard). I'd shoo him away and didn't think much more about it. Then we started to see him in the back yard. And eventually, I caught him in the house a couple times. Long story short, it's been probably a couple years now, and he clearly considers our house 'home'. We gave up trying to keep him away because he really is a sweet cat. The neighbor across the street says he still visits her place nightly, because she leaves food out for him on the porch. Apparently he's been around for a long time, and she had him neutered some time back.
He's a prolific hunter, but thankfully has stopped bringing us presents... likely because he's getting plenty to eat now. He's a 'kill to eat' cat. The female is a 'catch and play with, maybe kill' cat. She HATES him. Still. No longer coming to blows, but plenty of hissing and carrying by female if male gets too close.